It does, but it's avoided if possible. http://esperanto.davidgsimpson.com/eo-verbforms.html
Pobably not since Esperanto is a conlang with no specific culture assigned to it so unless there was a set of sayings and expresions created for the language even a simple expresion like the ones you are suggesting would only be understood if said expresion existed in that persons idiomatic lexicon. Hope that makes sense.
Esperanto was created that way (without a distinction between present and present continuous tenses). There is no other answer to that. You likely feel they are different because your native language has a distinction, but the distinction is much more technical than some (so probably the creator of Esperanto) find necessary.
I'm not able to contribute much of an argument. I'm not a native English speaker, but I just kind of assumed you can (almost) always abbreviate is to 's. It's going to the store. I'm at the library. The chest's open. The door's open (I've heard this a lot). I think the reason is because of the natural merge of i with whatever sound before.